Transcription of Introduction to Tensor Calculus for General Relativity
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Introduction to Tensor Calculus for General Relativity
Massachusetts Institute of Technology Department of Physics Physics Spring 1999. Introduction to Tensor Calculus for General Relativity c 1999 Edmund Bertschinger. All rights reserved. 1 Introduction There are three essential ideas underlying General Relativity (GR). The first is that space- time may be described as a curved, four-dimensional mathematical structure called a pseudo-Riemannian manifold. In brief, time and space together comprise a curved four- dimensional non-Euclidean geometry. Consequently, the practitioner of GR must be familiar with the fundamental geometrical properties of curved spacetime.
spaces is familiar to any student of quantum mechanics who has seen the Dirac bra-ket notation. Recall that the fundamental object in quantum mechanics is the state vector, represented by a ket |ψi in a linear vector space (Hilbert space). A distinct Hilbert space is given by the set of bra vectors hφ|. Bra vectors and ket vectors are linear ...
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